Labour stepped up its attack on the Liberal Democrat wing of David Cameron's coalition government by hinting Charles Kennedy, the former Lib Dem leader, has been in talks to defect to Labour and take several of his party colleagues with him.

Senior Lib Dems and allies of Kennedy were quick to dismiss rumours that he is poised to rejoin Labour – the party of his pre-SDP youth – as dirty tricks by rightwing bloggers seeking to destablise the coalition, though some MPs, also unhappy with coalition policies, admit "Charles is in a funny place at the moment."

Labour confirmed its ambition to woo any disaffected Lib Dems and claimed to have talked with Kennedy, who later dismissed the rumours as "the silliest of silly season stories".

But tonight near Glasgow – where Kennedy, newly separated from his wife, Sarah, has been spending the summer – Ed Miliband told supporters that if he wins the Labour leadership contest his strategy is to make the Lib Dems "extinct."

Speaking to Kilmarnock Labour party during a tour of Scottish constituencies, the younger Miliband urged Lib Dems to desert the party. "We have to make the Lib Dems an endangered species, and then extinct," he explained. Ironically, Kennedy, whose Highland seat was once Labour-held and remains anti-Tory, is thought to favour Ed Miliband's candidacy for Labour leader. Lib Dem MPs in Scotland and the North are aware how vulnerable unpopular coalition policies could make them among their constituents.

Miliband has been the most vociferous of the five candidates in his attack on Clegg's decision to form a government with the Tories. This week he said that should there be another inconclusive result at the next election, and a Lib-Lab pact becomes possible, a Labour party led by him would negotiate with Lib Dems only under a new leader, making Clegg's head the price of talks as Clegg did Gordon Brown's.

The issue is live since many Lib Dems believe that if there is a move to AV voting system after next year's referendum, coalitions could become a permanent option with Clegg's party zig-zagging between different governing allies.

In the volatile world of new coalition politics, Clegg signalled yesterday that he will not walk out of the coalition if next year's AV vote results in defeat for reform. "If [voters] say no, they have said no. It's an opportunity, finally – heaven knows we have been talking about this long enough." He added: "The Liberal Democrats aren't a sort of glorified form of the Electoral Reform Society" – a pointed reference to the most ardent advocates of reform.

But more critical Lib Dem MPs say that every twist of coalition policy adds to the strain. "They are putting a very generous interpretation on the coalition agreement," said one.

Today Miliband also wrote the Lib Dem leader saying that in sanctioning the appointment of Sir Philip Green as the government's new austerity tsar, Clegg had abandoned the commitment he made to tackle tax avoidance.

Miliband said: "You said, if in government, you would raise £2.4bn by attacking income tax avoidance, £1.4bn by halting abuse of corporation tax and a further £750m from stamp duty through tackling offshore registration by non-doms. You claimed your plans to clamp down on tax avoidance meant you would not need to raise VAT. However, since the election you have had a very different message for the country."